Indeed, you can see between 2011 and 2012 (for example) that Apple's PR site changed from calling it "Mac OS X" to simply calling it "OS X".
2011: https://web.archive.org/web/20111130104524/http://www.apple....
2012: https://web.archive.org/web/20111130104524/http://www.apple....
Interestingly Lion was called "Mac OS X Lion" upon release[0], but then their website[1] called it "OS X Lion" predominantly.
[0] https://www.apple.com/newsroom/2011/07/20Mac-OS-X-Lion-Avail...
[1] https://web.archive.org/web/20110705041542/http://www.apple....
2012 link is the same as the 2011 link.
Actual 2012 link: https://web.archive.org/web/20121207053101/http://www.apple....
It was clear that the OS wasn't thought of as a separate thing in the early days. The latest one looks like a typo.